Right Hand Man is a song sang primarily by Hamilton and Washington as they try to make a comeback after losing severely in the Revolutionary War.
We first start with Hamilton, who describes his desire for gory and legacy, but being a poor immigrant in a wealthy-dominated society, his only chance of being remembered in history is either reaching high ranks in the army or dying nobly on the battlefield to be remembered as a martyr (someone who dies but is remembered for being a hero). He expresses these thoughts through the lines "I knew that I was poor/I knew it was the only way to rise up" and "If they tell my story/I am either gonna die on the battlefield in glory or rise up".
Then we are introduced to George Washington, who is famous and celebrated by citizens and soldiers alike. Everyone greatly respects him ("Whose men are all lining up, to put me up on a pedestal"), but he himself knows that despite all the respect, he is losing this war ("The truth is in your face when you hear the British cannons go boom!").
A painting of American soldiers fighting against British red coats in the distance
As America starts losing ground in New York City, Washington searches for a right hand man who is competent enough to share his work, as there are too many things for Washington to manage at the same time. This is where Aaron Burr steps in and requests for the position of being Washington's right hand man. Unfortunately for him, Washington already had his eyes set on Hamilton, who expresses his wishes to continue fighting rather than be a secretary for other generals, to which Washington responds with "Dying is easy, young man, living is harder" (we will see similar phrases by Washington throughout the play later on).
Hamilton, given his personality and his principle of "not throwing away his shot", takes the position on the spot and immediately hires all his friends: Laurens, Mulligan, and Marquis de Lafayette (but notice how there's no Aaron Burr).